Complex numbers worksheet with answers

Free printable Complex numbers worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
ReIm55−5−5z₁z₂

For z₁ = −8 + j6 and z₂ = 2 − j3, find the modulus of the product, |z₁z₂|.

z₁ = −8 + j6z₂ = 2 − j3
|z₁z₂| =
2.Easy
ReIm11−1−122−2−233−3−3z₁z₂

For z₁ = 1 + j3 and z₂ = 2 − j2, find the imaginary part of the quotient z₁/z₂.

z₁ = 1 + j3z₂ = 2 − j2
Im(z₁/z₂) =
3.Medium
ReIm22−2−244−4−466−6−6θz

Find the argument θ of z = −6 − j in degrees, as the principal value between −180° and 180°.

z = −6 − j
θ = °
4.Medium
ReIm22−2−244−4−4θz

Find the argument θ of z = −1 + j4 in degrees, as the principal value between −180° and 180°.

z = −1 + j4
θ = °
5.Hard
ReIm11−1−122−2−2θz

Use De Moivre's theorem to find the real part of z⁹ for z = 2 + j2.

z = 2 + j2n = 9
Re(z⁹) =
6.Hard
ReIm11−1−122−2−2θz

Use De Moivre's theorem to find the imaginary part of z⁵ for z = √3 + j.

z = √3 + jn = 5
Im(z⁵) =

Answer key

  1. 1. |z₁z₂| = 36.06
  2. 2. Im(z₁/z₂) = 1
  3. 3. θ = −170.5 °
  4. 4. θ = 104 °
  5. 5. Re(z⁹) = 8192
  6. 6. Im(z⁵) = 16

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